#### Vol. 285, No. 2, 2016

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Conformal holonomy equals ambient holonomy

### Andreas Čap, A. Rod Gover, C. Robin Graham and Matthias Hammerl

Vol. 285 (2016), No. 2, 303–318
##### Abstract

We study the relation between two notions of holonomy on a conformal manifold. The first is the conformal holonomy, defined to be the holonomy of the normal tractor connection. The second is the holonomy of the Fefferman–Graham ambient metric of the conformal manifold. It is shown that the infinitesimal conformal holonomy and the infinitesimal ambient holonomy always agree up to the order that the ambient metric is defined.

##### Keywords
holonomy, ambient metric, tractor, conformal geometry
Primary: 53A30
Secondary: 53C29